Sarvesh K Verma Solutions for Chapter: Number System, Exercise 5: Introductory Exercise

The value of $4\times 100+3\times 10+\frac{9}{1000}$ is:

On the set of integers, if a$\mathrm{I}$ binary operation 'o' be defined as$\mathrm{aob}=\mathrm{a}-\mathrm{b}$ for every $\mathrm{a},\mathrm{b}\in \mathrm{I}$, then :

If $|\mathrm{x}-2|<3$ then :

How many of the following relations is/are always true for any real values of $\mathrm{p}$ and $\mathrm{q}$ ?

$\text{ (i) }|\mathrm{p}+\mathrm{q}|=\left|\mathrm{p}\right|+\left|\mathrm{q}\right|$

$\text{ (ii) }|\mathrm{p}-\mathrm{q}|=\left|\mathrm{p}\right|-\left|\mathrm{q}\right|$

  $\left(iii\right) \left|p/q\right| = \left|p\right|/\left|q\right|$

$\text{ (iv) }\left|\mathrm{pq}\right|=\left|\mathrm{p}\right|\left|\mathrm{q}\right|$

 (v)  $\left|{\mathrm{p}}^{\mathrm{q}}\right|=|\mathrm{p}{|}^{\left|\mathrm{q}\right|}$

$\text{ (vi) }\left|\sqrt[\mathrm{q}]{\mathrm{p}}\right|=\sqrt[\left|\mathrm{a}\right|]{\left|\mathrm{p}\right|}$

Which of the following relations is NOT always true?

The total number of integral values of $\mathrm{x}$ for which $\left|\right||\mathrm{x}-2|-4|-6|<10$

If $x$ satisfies $\left|x-1\right|+\left|x-2\right|+\left|x-3\right|\ge 6$, then:

Directions : In a test, conducted by Lamamia, a student attempted $\mathrm{n}$ problems out of total $30$problems and she scored net $17$marks. In this test each correct response awards $3$marks and each wrong response penalizes the test taker by deducting $1$mark from the total score.

If there are total m students who took the same test in which all the students scored net $17$marks and none of these students attempted same number of problems, what is the maximum value of m ?